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## Transient Elastography

Several techniques focus on the propagating shear waves resulting from a transient (impulsive or short tone burst) tissue excitation, whose displacement history along the central axial line can be extracted by ultrasonic techniques. This allows the global estimation of the tissue shear wave velocity and therefore the tissue elasticity.

### 1D Impulse Elastography

One-dimensional impulse elastography was born in 1994 during the PhD thesis of S. Catheline [29]. The idea consisted in measuring the tissue elasticity after exciting the tissue not monochromatically like in sonoelastography or MRE but by using a short impulsion. This technique allowed separating the compressional wave (which propagates very rapidly) from the slower shear wave without taking into account the boundary conditions. Therefore, the shear wave (generated by the pulse) displacement was no longer stroboscoped but recorded in real time by using a conventional ultrasound probe along the entire trajectory. Fig 1.10 illustrates a typical 1D impulse elastography setup.

#### 2D Impulse Elastography

Continuing with the development of the one-dimensional impulse elastography technique, some features were upgraded. In 1997, an echographic device used for acoustics time reversal experiments was adapted to perform ultrafast imaging [32] based on the emission of ultrasound plane waves. The system was composed of 128 independent emission\reception channels, each one with a 2 MB memory capacity. The ultrasound signals were sampled at 50 MHz. The transducer was fixed to a mechanical vibrator capable of generating shear waves within the medium at a frequency of 100 Hz (Fig 1.12 – right). The entire system was then controlled by a computer (Fig 1.12 – left). Once the shear wave propagation film was reconstructed, the inversion of the wave equation allowed the retrievalof the complete 2D Young’s modulus map of the medium. This system was known as twodimensional impulse elastography.

**Acoustic Radiation Force Imaging (ARFI)**

The ARFI or Acoustic Radiation Force Method is a dynamic elastography technique method developed by Nightingale et al. [40] in 2001, which uses acoustic radiation force to generate localized tissue displacements that are directly correlated with localized variations in tissue stiffness. These displacements are measured using ultrasonic correlation based methods and their magnitude is inversely proportional to the local tissue stiffness. In this method, focused ultrasound is used to apply localized radiation force (pushing) to small volumes of tissue (2 to 3 mm) for short durations (less than 1 ms). The resulting tissue displacements are mapped using ultrasonic correlation-based methods [40]. Therefore, the ARFI technique allows to track the tissue displacement and relaxation directly after the radiation force has been applied (Fig 1.15). The temporal properties of such relaxation curves permit the retrieval of information regarding the elasticity and viscosity at the focal point only [41]. Moreover, radiation force induced tissue displacements are generated at multiple locations and combined to build a complete quantitative map of tissue stiffness (Fig 1.16). This increases the time needed to build one entire image [42] as well as the tissue temperature due to multiple “pushing”. This technique has been used to build quantitative elasticity maps on breast , prostate and liver [43][44].

**The Supersonic Shear Wave Imaging (SSI) Technic**

The SSI technique is a step further in the development of the 2D impulse elastography technique [12]. This dynamic elastography technique born in 2004, utilizes radiation force to excite the medium and generate shear waves and ultrafast imaging to track their displacement. The idea of associating radiation force to the study of generated shear waves comes from Sarvazyan, who introduced the concept of Shear Wave Elasticity Imaging (SWE) in 1998 [46]. It was in 2004 that Bercoff [47] combined two fundamental ideas to overcome the limitations encountered by the 2D elastography technique. These two concepts, radiation force and ultrafast shear wave imaging are the base of the Supersonic Shear Imaging technique. The technique can be subdivided into two basic steps as follows:

The Mach-cone creation: ultrasound waves are focalised successively at different depths to create spherical waves at each focal point. All the generated spherical waves interfere constructively to create a sort of Mach-cone [12] (quasi-plane on the imaging plane and cylindrical in three dimensions) which propagates in opposite directions (Fig 1.17(a)). The constructive spherical wave interference increases the shear wave amplitude and the signal to noiseratio. In the imaging plane, the plane wave front allows the simplification ofpropagation hypotheses, which is of great interest for the inverse problem. Only one Mach-cone is needed to generate the quasi-plane shear wave fronts that travel across the medium to cover the entire region of interest.

Ultrafast Imaging: ultrasound plane waves are generated to track the shear wave displacement along the entire imaging plane. During a single acquisition, up to 8000 images per second can be acquired. Hence, only one Mach-cone is enough to acquire the complete 2D shear velocity map of the medium (Fig 1.17(b)).

In the SSI technique, the external vibrator employed to generate the shear waves in the 2D impulse elastography technique is replaced by the acoustic radiation force. Therefore, both the excitation and imaging processes are carried out using an ultrasound probe. The generated shear waves have an amplitude (from 0 to the maximum) of several dozens of micrometres and are detectable with a good signal to noise ratio by axial correlation and ultrafast imaging. The latter allows to perform an entire single acquisition in less than 30 ms, imaging in real time the shear wave displacement and permitting the retrieval of the shear wave velocity and the complete 2D quantitative elasticity map of the medium (using Eq. 2 and Eq. 5) with great precision. The Spatial resolution of the elasticity maps obtained with this technique at 8 MHz and 15 MHz are of 1.2 mm and 0.4 mm respectively.

**Table of contents :**

General Introduction

**1. Chapter 1. Elastography: an important medical imaging research field **

1.1 Introduction

1.1.1 Static Elastography

1.1.2 Dynamic Elastography

1.1.2.1 Monocromatic

1.1.2.1.1 Sonoelastography

1.1.2.1.2 Magnetic Resonance Elastography (MRE)

1.1.2.1.3 Vibro-acoustography

1.1.2.2 Transient Elastography

1.1.2.2.1 1D Impulse Elastography

1.1.2.2.2 2D Impulse Elastography

1.1.2.2.3 Acoustic Radiation Force Imaging (ARFI)

1.1.2.2.4 The Supersonic Shear Wave Imaging (SSI) Technic

1.2 Conclusion

**2. Chapter 2. Monitoring Chemotherapy treatment by using 3D-Shear Wave Elastography (3D-SWE) **

2.1 Introduction

2.2 Materials and Methods

2.2.1 Clinical protocol

2.2.2 3D-Ultrasound (3D-US)

2.2.3 3D-Shear Wave Ultrasound Elastography (3D-SWE)

2.2.4 Magnetic Resonance Imaging (MRI)

2.2.5 Statistical analysis.

2.3 Results

2.3.1 Protocol I

2.3.1.1 Statistical analysis

2.3.2 Protocol II

2.3.2.1 Tumour volume

2.3.2.2 Tumour elasticity

2.4 Discussion

2.5 Conclusion

**3. Chapter 3. What is the pathology underlying stiffness? **

3.1 Materials and Methods

3.1.1 Tumour growth phase

3.1.1.1 Tumour model

3.1.1.2 2D-Ultrasound and the Supersonic Shear Wave Imaging (SSI) technique

3.1.1.3 In vivo/ex vivo comparison of elasticity values

3.1.1.4 Pathological analysis

3.1.1.5 Statistical analysis

3.1.2 Tumour treatment by chemotherapy

3.2 Results

3.2.1 Tumour growth

3.2.1.1 Tumour model

3.2.1.2 The Supersonic Shear Wave Imaging (SSI) technique

3.2.1.3 In vivo/ex vivo comparison of elasticity values

3.2.1.4 Pathology

3.2.2 Tumour treatment by chemotherapy

3.3 Discussion

3.4 Conclusion

**4 Chapter 4. Characterization of ectopic and orthotopic colon carcinoma CT26 using Ultrasound and the Supersonic Shear Wave Imaging (SSI) technique **

4.1 Introduction

4.2 Materials and Methods

4.2.1 CT26 tumour model

4.2.2 Histological tumour cellularity and Micro Vascular Density characterization

4.2.3 Animals

4.2.4 Ectopic tumour implantation

4.2.5 Orthotopic tumour implantation

4.2.6 Combretastatin A4 Phosfate treatment

4.2.7 2D-US and the SSI technique

4.2.8 In vivo calliper measurements

4.2.9 Statistical analysis

4.3 Results

4.3.1 Measurement of the tumour volume and elasticity

4.3.1.1 Tumour volume

4.3.1.2 Tumour elasticity

4.4 Discussion

4.5 Conclusion

**5. Chapter 5. Nonlinear shear elastic parameter quantification **

5.1 Introduction

5.2 Materials and Methods

5.2.1 Acoustoelasticity theory

5.2.2 Experimental Setup

5.2.3 Imaging techniques and finite element simulation

5.2.3.1 Shear modulus computation using the Supersonic Shear Imaging technique

5.2.3.2 Displacement and Strain maps computation using the static elastography technique

5.2.3.3 Stress computation combining static elastography and SSI measurements

5.2.3.4 Nonlinear shear modulus (A) calculation

5.2.4 Finite element simulation

5.3 Results

5.3.1 Experimental and simulated cumulative Strain maps

5.3.2 Experimental and simulated cumulative stress maps

5.3.3 Nonlinear shear modulus maps in agar-gelatin phantoms

5.3.4 Nonlinear shear modulus maps in ex vivo beef liver samples

5.4 Ex vivo application

5.4.1 Ex vivo strain and stress calculation in mouse colon tissues

5.4.1.1 US Imaging

5.4.1.2 Animal preparation

5.5 Discussion

5.6 Conclusion

**References**